Simplify the following expression: $\dfrac{12t^5}{9t^3}$ You can assume $t \neq 0$.
$ \dfrac{12t^5}{9t^3} = \dfrac{12}{9} \cdot \dfrac{t^5}{t^3} $ To simplify $\frac{12}{9}$ , find the greatest common factor (GCD) of $12$ and $9$ $12 = 2 \cdot 2 \cdot 3$ $9 = 3 \cdot 3$ $ \mbox{GCD}(12, 9) = 3 $ $ \dfrac{12}{9} \cdot \dfrac{t^5}{t^3} = \dfrac{3 \cdot 4}{3 \cdot 3} \cdot \dfrac{t^5}{t^3} $ $\phantom{ \dfrac{12}{9} \cdot \dfrac{5}{3}} = \dfrac{4}{3} \cdot \dfrac{t^5}{t^3} $ $ \dfrac{t^5}{t^3} = \dfrac{t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t} = t^2 $ $ \dfrac{4}{3} \cdot t^2 = \dfrac{4t^2}{3} $